Two numbers and Alex and Bill
Alex asks Bill to guess two 3-digit positive integers. Alex then told Bill about the properties of these two numbers, which are as follows:
- The absolute difference between these two numbers is 288.
- The sum of digits of each of these two numbers is both 12.
- All the 6-digits used in these two numbers are distinct non-zero digits.
After that, Bill did some working and found out that there are multiple solutions and told Alex that it is impossible to answer this question. Alex agreed and told Bill that Alex is going to write the last digit of the sum on a piece of paper and after that indeed Alex took a piece of paper and wrote that digit of the sum, digit which is not known to us readers but which Alex promised will help Bill anyway.
Given this extra information, Bill figured out these two numbers. What are the values of these two numbers?
Submit your answer as the sum of these two numbers.